Velocity field of the fully developed laminar flow in a hexagonal duct

The paper presents a study concerning the velocity field of the fully developed laminar flow in a hexagonal duct. This duct is the main part of an actuator–sensor structure used for the determination of fluid and flow parameters. The particular shape of the duct is determined by silicon technology. The central subject detailed herein is the building of an approximative analytical formula for the velocity field inside hexagonal ducts. We detail two approaches for this subject and we discuss their limitations in the practical circumstances by using the CFD-ACE+ software package for the fluid flow simulation. One approach is based on the point-matching method and another one is based on the generalised integral transform method. The both approaches are offering similar credibility, namely the maximum errors produced by using these formulae are, respectively, 5 and 12% for the middle part of the cross-section where the actuators and sensors are usually placed. The second approach is more suitable for flatter ducts or when the designer is interested in a small central region of the cross-section. The simple applicability of the inferred formulae contrasts with the classical and huge time consuming numerical approaches, these formulae being suitable tools in the design process of the structure operating in the micro-world. The results presented in this paper might be adapted for similar structures operating in the macro-world where devices containing ducts having various non-circular cross-sections are present and where the fully developed laminar flow of the incompressible and Newtonian fluids is concerned.